Finite Group Databasebeta

← #29590867

Subgroups — #29590867

Order 15616.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456564C211yesmaximal, characteristic
2#21445968C211yesmaximal, characteristic
3#21443814C212yesmaximal
4#21443808C212yesmaximal
5C61×#2165C211yesmaximal, characteristic
6#16840319—21no—
7#16840160C411yescharacteristic, complemented
8#16840142C411yescharacteristic, complemented
9#16840113—21no—
10#16840020—21no—
11#16840020C2212yes—
12#16839870—21no—
13#16839870C412yescomplemented
14#16839533—21no—
15#16839522—21no—
16#16839520C2211yescharacteristic
17#16839519C2211yescharacteristic
18C4×M16×C61C2211yescharacteristic
19C61×#364—21no—
20C61×#349C2212yes—
21C61×#347—21no—
22C2×Dic244—21no—
23C2×Dic244C2×C412yes—
24C2×#11758194—21no—
25#14519777—21no—
26#14519777—21no—
27#14519769—41no—
28#14519756—22no—
29#14519756—41no—
30C4×Dic122—22no—
31C4×Dic122—41no—
32#14519736—21no—
33#14519736—41no—
34#14519709—21no—
35#14519709C2×C412yes—
36#14519702—22no—
37#14519702—22no—
38C2×M16×C61D411yescharacteristic
39C2×M16×C61C2311yescharacteristic
40C2×C42×C61D411yescharacteristic
41M32×C61—22no—
42#97×C61C2×C411yescharacteristic
43#97×C61D411yescharacteristic
44C4×C8×C61C2×C411yescharacteristic
45C4×C8×C61D411yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2×D411yescharacteristic
48C2×Dic122—22no—
49C2×Dic122—41no—
50M16×C61—41no—
51M16×C61—41no—
52C2×C8×C61C22⋊C411yescharacteristic
53C2×C8×C61C22⋊C411yescharacteristic
54C2×C8×C61C22×C411yescharacteristic
55C2×C8×C61C2×D411yescharacteristic
56C42×C61—21no—
57C42×C61C22⋊C411yescharacteristic
58C42×C61C22⋊C411yescharacteristic
59C22⋊Dic61—42no—
60C22⋊Dic61—41no—
61C4⋊Dic61—22no—
62C4⋊Dic61—41no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65C4⋊Dic61—41no—
66#11758196—42no—
67#11758196—42no—
68C4×Dic61—42no—
69C4×Dic61—41no—
70#11758194—41no—
71#11758194—41no—
72C2×#92418—41no—
73Dic244—42no—
74Dic244—42no—
75C16×C61—42no—
76C23×C61AGL(1,ℤ/8)11yescharacteristic
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—42no—
82C2×C4×C61C2×C22⋊C411yescharacteristic
83C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—81no—
87Dic122—42no—
88Dic122—42no—
89Dic122—82no—
90C8×C61—21no—
91C8×C61—21no—
92C8×C61—21no—
93C8×C61—21no—
94#92418—81no—
95#11838—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—41no—
98C22×C61#41811yescharacteristic
99C4×C61—22no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61#41011yescharacteristic
103C4×C61#42111yescharacteristic
104Dic61—82no—
105Dic61—82no—
106Dic61—161no—
107#3185—611no—
108#2165D6111yescharacteristic
109#1841—611no—
110#1342—612no—
111#1340—612no—
112C2×C61—21no—
113C2×C61—41no—
114C2×C61#151411yescharacteristic
115#533—1221no—
116#498—611no—
117#494—611no—
118#487—1221no—
119#470—612no—
120#470—1221no—
121#441—612no—
122#441—1221no—
123C4×M16C2×D6111yescharacteristic
124#364—21no—
125#349C2×D6112yes—
126#347—21no—
127#344—1221no—
128#339—1221no—
129#338—611no—
130H(3,ℤ/4)—611no—
131C61#1183811yescharacteristic, complemented, Sylow
132C2×Q16—612no—
133C2×Q16—1221no—
134C2×M16—1221no—
135C2×M16D24411yescharacteristic
136C2×M16C22×D6111yescharacteristic
137C4⋊Q8—1221no—
138C4⋊Q8—1221no—
139#125—2441no—
140C22⋊Q8—1222no—
141C22⋊Q8—2441no—
142C4×Q8—1222no—
143C4×Q8—2441no—
144#117—1221no—
145#117—2441no—
146C2×C42D24411yescharacteristic
147M32—22no—
148#106—612no—
149#106—1221no—
150#103—1222no—
151#103—1222no—
152#97C4×D6111yescharacteristic
153#97C22⋊D6111yescharacteristic
154C4×C8C4×D6111yescharacteristic
155C4×C8C22⋊D6111yescharacteristic
156C2×Q8—1222no—
157C2×Q8—2441no—
158C22×C4—21no—
159C22×C4C2×D24411yescharacteristic
160Q16—2442no—
161Q16—2442no—
162M16—41no—
163M16—41no—
164M16—2441no—
165M16—2441no—
166C2×C8—2441no—
167C2×C8#1175819811yescharacteristic
168C2×C8#1175819811yescharacteristic
169C2×C8C2×C4×D6111yescharacteristic
170C2×C8C2×C22⋊D6111yescharacteristic
171C4⋊C4—1222no—
172C4⋊C4—2441no—
173C4⋊C4—2442no—
174C4⋊C4—2441no—
175C4⋊C4—2441no—
176C4⋊C4—2441no—
177C4⋊C4—2442no—
178C22⋊C4—2441no—
179C22⋊C4—2442no—
180C42—21no—
181C42—2441no—
182C42—2442no—
183C42#1175819811yescharacteristic
184C42#1175819811yescharacteristic
185C16—42no—
186C23#1451980511yescharacteristic
187Q8—4882no—
188Q8—2442no—
189Q8—2442no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—4881no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4C2×#1175819811yescharacteristic
199C2×C4#1451980511yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—4881no—
205C22—21no—
206C22—41no—
207C22#1683976811yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—9761no—
212C4—4882no—
213C4—4882no—
214C4#1683973511yescharacteristic
215C4#1683977811yescharacteristic
216C2—21no—
217C2—41no—
218C2#2144436711yescharacteristic
subgroupG/H
centerC2#21444367
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#2165C2
socleC2×C61#1514
prime radicalC23×C61AGL(1,ℤ/8)
cosocleC2×M16×C61C23
hypercenter#2165D61
hypocenterC61#11838
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
7. #16840160C4semidirect
8. #16840142C4semidirect
13. #16839870C4semidirect
131. C61#11838semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214565642
#214459682
#214438142
#214438082
C61×#21652
#1183861